CN108808426B - An Inverse Smith-Purcell Radiation Source Based on Photonic Crystal and Grating Combination and Its Generation Method - Google Patents

Abstract

The invention discloses an inverse Smith-Purcell radiation source based on a photonic crystal and grating combined structure and a generation method thereof. The invention combines the photonic crystal and the grating, utilizes the negative refraction characteristic of the photonic crystal to realize the effect of inverse Smith-Purcell (SP) radiation, and establishes a novel terahertz radiation source.

Description

An inverse Smith-Purcell radiation source based on the combination of photonic crystal and grating and production method

technical field

The invention belongs to the technical field of vacuum electronics, in particular to an inverse Smith-Purcell radiation source based on a photonic crystal and a grating combined structure.

Background technique

The special frequency band of terahertz waves (between light waves and microwaves) can be divided into two categories: electronic methods and optical methods. The terahertz sources obtained by electronic methods (such as electron gyrotrons, anti-wave tubes, etc.) can only generate lower frequency bands in the terahertz frequency band due to their high conversion efficiency, and the tuning range is limited. Hertzian waves. Optical methods mostly use parametric oscillation or difference frequency to obtain terahertz waves, such as terahertz gas lasers, THz wave radiation sources with optical rectification effect, etc. Although the coherence ratio is good, it can generate terahertz waves above 1THz, but terahertz waves The wave power is lower than the former.

SUMMARY OF THE INVENTION

In order to improve the frequency tunability of the THz radiation source, improve the radiation wave collection efficiency, and reduce the volume of the radiation source, the invention provides an inverse Smith-Purcell radiation source and an inverse Smith-Purcell radiation source based on the combined structure of photonic crystal and grating. The production method combines photonic crystals with gratings, utilizes the negative refraction characteristics of photonic crystals, realizes the effect of inverse Smith-Purcell (SP) radiation, and establishes a new type of terahertz radiation source.

In order to achieve the above object, the technical scheme adopted in the present invention is:

An inverse Smith-Purcell radiation source based on a photonic crystal and grating combined structure, comprising an electron gun, a metal grating and a photonic crystal, the electron gun is arranged on one side of the metal grating, and the photonic crystal is arranged on the other side of the metal grating , the photonic crystal has negative refraction characteristics.

Further, the photonic crystal is a structure of triangular arrangement of air columns.

Further, the lattice constant a of the photonic crystal is 630um, and the radius of the air column is 0.45a.

Further, the period of the metal grating is 118um, the height is 100um, and the duty ratio is 1:1.

Further, the thickness of the photonic crystal and the grating is 500um, and the distance between the photonic crystal and the grating is 375um.

The present invention also provides a method for generating an inverse Smith-Purcell radiation source, comprising:

计算出对应结构的SP频率范围，SP公式中，L为光栅周期，β为电子相对论速度与光速的壁纸，θ为观测点与电子运动方向的夹角，n为谐波次数；First use the SP formula

Calculate the SP frequency range of the corresponding structure. In the SP formula, L is the grating period, β is the wallpaper of the electron’s relativistic velocity and the speed of light, θ is the angle between the observation point and the electron’s motion direction, and n is the harmonic order;

Then use the plane wave expansion method to calculate the energy band structure and isofrequency diagram of the photonic crystal. The eigen equation of the plane wave expansion in the TM wave is:

为傅立叶展开系数，A(k_//|G_//)为列向量，k_//为波矢，本征方程的左边为一个关于对角线对称的正定矩阵，因此本征方程的所有特征根全部是正数，将

看成是左边矩阵的特征根λ，所以

where k _// =k _x e _x + _ky e _y , G _// =b ₁ e _x +b ₂ e _y ,

is the Fourier expansion coefficient, A(k _// |G _// ) is the column vector, k _// is the wave vector, and the left side of the eigen equation is a positive definite matrix that is symmetrical about the diagonal, so all the characteristic roots of the eigen equation are all positive numbers, the

regarded as the characteristic root λ of the left matrix, so

Through the energy band structure and isofrequency diagram of the photonic crystal, find out the part that can satisfy the opposite direction of the group velocity and the wave vector in the SP frequency range, vg·k<0, that is, the part that can realize negative refraction in the photonic crystal, and then put the part with Photonic crystals with negative refractive properties are combined with gratings to realize the inverse SP phenomenon.

Owing to adopting the above-mentioned technical scheme, the beneficial effects of the present invention are:

The invention combines the grating with the photonic crystal, utilizes the negative refraction property of the photonic crystal, modulates the parameters of the photonic crystal through the dispersion characteristics of the photonic crystal and the iso-frequency diagram, etc. The frequencies are matched to obtain reverse SP radiation; the reverse SP radiation is further modulated and collected to become a new type of radiation source. The photonic crystal and the electron column are distributed on both sides of the grating respectively, which can prevent the direct contact between the electron column and the photonic crystal, and prevent the electron column from directly exciting the SP radiation of the photonic crystal.

Description of drawings

1 is a schematic structural diagram of an inverse Smith-Purcell radiation source based on a photonic crystal and grating combined structure of the present invention;

FIG. 2 is a schematic diagram of the propagation of the SP of the present invention in the photonic crystal structure.

Reference numerals: 1 - electron gun, 2 - grating, 3 - photonic crystal, 4 - electron note.

Detailed ways

1, FIG. 2, the structure of the reverse Smith-Purcell radiation source of the present invention is made up of an electron gun 1, a metal grating 2 and a photonic crystal 3, the electrons generated by the electron gun 4, the electron gun 1 and the photonic crystal 3 are respectively in the metal grating 2. sides. In this structure, the photonic crystal 3 is a photonic crystal arranged in a triangle of air columns, the lattice constant a of the photonic crystal 3 is 630um, and the radius of the air column is 0.45*a. The period of metal grating 2 is 118um, the height is 100um, and the duty ratio is 1:1. The thicknesses of the photonic crystal 3 and the metal grating 2 are both 500um, and the distance between the photonic crystal 3 and the metal grating 2 is 375um. Electron gun 1 voltage is 3kv. The electrons emitted by the electron gun 1 generate spontaneous incoherent Smith-Purcell radiation on the surface of the metal grating 2 , and the SP radiation leaks to the other side of the metal grating 2 through the holes of the metal grating 2 and enters the interior of the photonic crystal 3 . In photonic crystal 3, in some special frequency bands, due to the periodic modulation of the incident electromagnetic wave by the refractive index of the material, the direction of the phase velocity and the direction of the group velocity of the electromagnetic wave propagating in the photonic crystal may be opposite. properties of negatively refracting media. The SP flips inside the photonic crystal with this negative refraction characteristic, high frequency becomes low frequency, and low frequency changes to high frequency, realizing the reverse Smith-Purcell radiation phenomenon.

The structure of the inverse Smith-Purcell radiation source of the present invention can realize inverse Smith-Purcell radiation in the millimeter wave, submillimeter wave and terahertz wavebands.

The production method of the reverse Smith-Purcell radiation source of the present invention comprises:

计算出对应结构的SP频率范围，SP公式中，L为光栅周期，β为电子相对论速度与光速的壁纸，θ为观测点与电子运动方向的夹角，n为谐波次数；First use the SP formula

Calculate the SP frequency range of the corresponding structure. In the SP formula, L is the grating period, β is the wallpaper of the electron’s relativistic velocity and the speed of light, θ is the angle between the observation point and the electron’s motion direction, and n is the harmonic order;

Then use the plane wave expansion method to calculate the energy band structure and isofrequency diagram of the photonic crystal. The eigen equation of the plane wave expansion in the TM wave is:

为傅立叶展开系数，A(k_//|G_//)为列向量，k_//为波矢，本征方程的左边为一个关于对角线对称的正定矩阵，因此本征方程的所有特征根全部是正数，将

看成是左边矩阵的特征根λ，所以

where k _// =k _x e _x + _ky e _y , G _// =b ₁ e _x +b ₂ e _y ,

is the Fourier expansion coefficient, A(k _// |G _// ) is the column vector, k _// is the wave vector, and the left side of the eigen equation is a positive definite matrix that is symmetrical about the diagonal, so all the characteristic roots of the eigen equation are all positive numbers, the

regarded as the characteristic root λ of the left matrix, so

Through the energy band structure and isofrequency diagram of the photonic crystal, find out the part that can satisfy the opposite direction of the group velocity and the wave vector in the SP frequency range, vg·k<0, that is, the part that can realize negative refraction in the photonic crystal, and then put the part with Photonic crystals with negative refractive properties are combined with gratings to realize the inverse SP phenomenon.

As shown in Figure 2, the schematic diagram of SP propagation in the structure, the x-axis represents the position of the grating, the O point is the position of the electron at this time, and the direction of electron movement is from left to right. The upper half space of the x-axis is the photonic crystal part, and the lower half space is the vacuum part. The lower half space is normal SP radiation. It can be seen that the frequency changes from high to low from front to back in the direction of electron movement, which is in line with the SP formula. The upper half space is the unusual SP radiation in the photonic crystal, which is manifested as the extraordinary inverse SP radiation from the front to the back of the electron movement direction, from the middle frequency to the low frequency, and then from the high frequency to the low frequency. The structure can realize inverse SP radiation to achieve efficient collection of SP, and then process it into a new type of SP THz radiation source.

Claims (6)

1. an inverse Smith-Purcell radiation source based on photonic crystal and grating combination, comprises electron gun, metal grating and photonic crystal, described electron gun is arranged on one side of metal grating, and described photonic crystal is arranged on another side of metal grating. side, characterized in that the photonic crystal has negative refraction characteristics. 2 . The inverse Smith-Purcell radiation source according to claim 1 , wherein the photonic crystal is a triangular arrangement of air columns. 3 . 3. The inverse Smith-Purcell radiation source according to claim 2, wherein the lattice constant a of the photonic crystal is 630um, and the air column radius is 0.45a. 4 . The inverse Smith-Purcell radiation source according to claim 1 , wherein the period of the metal grating is 118um, the height is 100um, and the duty ratio is 1:1. 5 . 5. The inverse Smith-Purcell radiation source according to claim 1, wherein the thickness of the photonic crystal and the grating is 500um, and the distance between the photonic crystal and the grating is 375um. 6. a method for utilizing the inverse Smith-Purcell radiation source of the inverse Smith-Purcell radiation source based on the combination of photonic crystal and grating as described in any one of claims 1-5, is characterized in that, comprising: First use the SP formula

Calculate the SP frequency range of the corresponding structure. In the SP formula, L is the grating period, β is the ratio of the electron’s relativistic velocity to the speed of light, θ is the angle between the observation point and the electron’s motion direction, and n is the harmonic order; Then use the plane wave expansion method to calculate the energy band structure and isofrequency diagram of the photonic crystal. The eigen equation of the plane wave expansion in the TM wave is:

where k _// =k _x e _x + _ky e _y , G _// =b ₁ e _x +b ₂ e _y ,

is the Fourier expansion coefficient, A(k _// |G _// ) is the column vector, k _// is the wave vector, and the left side of the eigen equation is a positive definite matrix that is symmetrical about the diagonal, so all the characteristic roots of the eigen equation are all positive numbers, the

regarded as the characteristic root λ of the left matrix, so

Through the energy band structure and isofrequency diagram of the photonic crystal, find out the part that can satisfy the opposite direction of the group velocity and the wave vector in the SP frequency range, vg·k<0, that is, the part that can realize negative refraction in the photonic crystal, and then put the part with Photonic crystals with negative refractive properties are combined with gratings to realize the inverse SP phenomenon.

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